Does special relativity prevail inside relativistic particles? Yes!

Y. S. Kim
Department of Physics
University of Maryland


When Einstein formulated special relativity 99 years ago, he derived his energy-momentum relation for point particles, which is valid for both slow, fast, and massless particles. Since then, particles were found to have internal space-time structures, such as spin, helicity, and gauge degrees of freedom. By introducing the little groups of the Poincare group, Eugene Wigner laid the mathematic foundations for the internal space-time symmetries of relativistic particles. By 1990, it was shown that Wigner's little groups are capable of unifying the internal space-time symmetries of relativistic particles [Kim and Wigner, J. Math. Phys. Vol. 31, page 55-60 (1990)].

For instance, massive and slow particles have spin degrees of freedom, while massless particles have helicity and gauge degrees of freedom. It was shown that they can be unified into a single covariant entity, as Einstein's energy-momentum relation does for massive and massless particles.

Some of relativistic particles, such as protons and neutrons, are known to have space-time extensions. According to Gell-Mann, they are bound states of quarks (like hydrogen atom). According to Feynman, they are collections of free massless particles called "partons." The quark model is valid only for massive and slow particles, while the parton model is valid only for particles moving with speed close to that of light. The question then is whether these seemingly different pictures are two different manifestations of a single covariant entity? This question is addressed in this report. Here again, Einstein prevails. Please visit

for a more detailed explanation.

The author had a privilege of working with Eugene Wigner in his late years. He was able to hear from him about Immanuel Kant's influence on Einstein and also on himself. This aspect will also be discussed if there is sufficient time.